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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, February 2, 2017 - 3:00pm

Dominic Searles



University of Pennsylvania


We introduce the combinatorial model of Kohnert tableaux, based on the diagram model of A. Kohnert. We use Kohnert tableaux to introduce the quasi-key basis of the polynomial ring, which lifts the quasi-Schur polynomials of Haglund, Luoto, Mason and van Willigenburg. Key polynomials expand positively in quasi-key polynomials which in turn expand positively in fundamental slide polynomials. We give simple combinatorial formulas for these expansions in terms of Kohnert tableaux, lifting the parallel expansions of a Schur polynomial into quasi-Schur polynomials into fundamental quasisymmetric polynomials. (Joint work with S. Assaf.)